engleski

Heavy-tailed modeling of CROBEX

Classical continuous-time models for log-returns usually assume their independence and normality of distribution. However, nowadays it is widely accepted that the empirical properties of log-returns often show a specific correlation structure and deviation from normality, in most cases suggesting that their distribution is heavy-tailed. Therefore we suggest an alternative continuous-time model for log-returns, a diffusion process with Student’s marginal distributions and exponentially decaying autocorrelation structure. This model depends on several unknown parameters that need to be estimated. The tail index is estimated by the method based on the empirical scaling function, while the parameters describing mean, variance and correlation structure are estimated by the method of moments. The model is applied to the CROBEX stock market index, meaning that the estimation of parameters is based on the CROBEX log-returns. Quality of the model is assessed by the means of simulations, by comparing CROBEX log-returns with the simulated trajectories of the Student’s diffusion depending on estimated parameter values.

Log-return; Heavy-tailed distribution; Student’s distribution; Diffusion process; Geometric Brownian motion

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